Transcript Equity, Access, and Productive Learning

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SVMI PROFESSIONAL DEVELOPMENT
November 13, 2012
hosted by Dublin Unified School District
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 CCSS
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Agenda
Standards for Mathematical Practice
 CCSS Grade Level Overviews
 Differentiation
 Van Hiele & Mosaic Puzzles
 Menu Slices and FALs
 Lunch
 Breakout Groups
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1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of
others.
4.
Model with mathematics.
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Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Grouping the Practices
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William McCallum
Standards for
Mathematical
Practice
Tucson, April 2011
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Grouping the Practices
 SMP
Pairs
1 & 6 ; 2 & 3 ; 4 & 5 ; 7 & 8
 Discuss
with your SMP partner the
similarities and differences between the two
practices in the K-1 posters and then the
middle school posters.
 Discuss
with your SMP partner why these
two practices have been grouped
together.
 Share
highlights of your partner talk with
your table.
 Whole
group discussion
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Geometry Across Grade Levels
In
your team of 8:
 Read
one of the overview handouts (K/1;
2/3; 4/5, 6, 7, 8, Algebra, Geometry)
 Circle, underline, or, highlight any
geometry concepts and other big ideas that
support geometrical reasoning.
 Share the progression of geometry with
your table, beginning with the K/1
overview.
 Popcorn share out and clarifying questions.
CCSS-Mathematics
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Content
paint
standards:
the Big Picture of the domain
flesh out the domain
are not a checklist
are independent of California’s 1997
math standards
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Differentiation
Please
read Malcolm Swan’s
Improving Learning in Mathematics:
Challenges and Strategies
Discuss
at your table:
highlights from the article.
 anything that resonated with you.
 questions that arose while reading .
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Whole
Group Debrief
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Setting the Stage for Geometry
Take
a few minutes to think about
and represent in some way
[diagraming, webbing, listing,
organizing] what you believe are the
big ideas in Geometry.
Pair/Share
your ideas with an elbow
partner
Group
Popcorn Sharing
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Setting the Stage for Geometry
Please
read the excerpts from
Van de Walle and Burns.
Discuss
at your table:
highlights from the article.
 anything that resonated with you.
 questions that arose while reading .
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Whole
Group Debrief
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Van Hiele Levels
“I
believe that development is more
dependent on instruction than on age
or biological maturation and that
types of instructional experiences
can foster, or impede, development.”
-Pierre M. van Hiele
Teaching Children Mathematics
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Van Hiele Levels
Please
read Van Hiele’s Levels of
Geometric Reasoning
Level 0
Level 1
Level 2
Level 3
Level 4
Recognition
Analysis
Informal Deduction
Formal Deduction
Rigor
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Level 0
Shapes are what they look like
Students
recognize and name
figures based on the global visual
characteristics of the figure.
It’s
a square because it looks like a
house.
These shapes go together because
they’re pointy or they’re fat.
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Work of 10th grader
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Work of 10th grader
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Instruction at Level 0
Sorting
and Classifying-see how
shapes are alike and different
Variety
of shapes- minimize the effect
of irrelevant features. Build activities
around specific properties so students
start to understand and see them
naturally.
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Questions at Level O
Let’s
see if that’s true for other
rectangles.
Can
you draw a triangle that does not
have a right angle?
In general students should be challenged
to see if observations made about a
particular shape apply to other similar
shapes.
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Level 1- Analysis
Students
start to see classes of shapes
(instead of a rectangle, all rectangles)
Start
to see properties of shapes or list of
attributes
They
have trouble with subcategories or
sifting through the attributes, such as
seeing that squares are also rectangles,
quadrilaterals, parallelograms.
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What’s a rectangle?
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6th graders were asked: Can a parallelogram be both a
rectangle and a rhombus?
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What’s a rectangle?
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6th graders were asked: Can a parallelogram be both a
rectangle and a rhombus?
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What’s a rectangle?
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6th graders were asked: Can a parallelogram be both a
rectangle and a rhombus?
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Student Finds Correct Attributes
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Other Students
 Did
not notice that Blobbies had 4 sides.
 Failed
to notice that Blobbies had circles
in the middle or thought all shapes with
circles in the middle were Blobbies.
 Students
used irrelevant properties like
parallel sides.
 Students
couldn’t sort with 2 attributes.
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Instruction at Level 1
Focus
on properties rather than mere
identification.
Think
about classes: all rectangles, all
prisms.
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Questions at Level 1
Questions
that involve reasoning:
If the sides of a four-sided shape are
all congruent, will you always have a
square? How do you know?
 Can you find a counterexample? How
do you know?
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Instruction at Level 2
 Make
and test hypotheses and
conjectures.
 Examine
properties of shapes to
determine necessary and sufficient
conditions.
 Use
language of informal deduction: all,
some, none, if-then, what if, etc.
 Encourage
proofs.
students to attempt informal
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Implications for Instruction
Handout
 Students
working at the recognition or
visual level needed activities like…
 Students working at this analysis stage
need activities like…
 Students working at abstraction or
informal deduction are ready for…
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Mosaic Puzzle
Please
cut out the puzzle pieces and
explore their relationships.
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Mosaic Puzzle
Find
all the pieces that can be made
from two other pieces.
Find all the pieces that can be made
from three other pieces.
How many different shapes can be
made with a pair of pieces?
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Mosaic Puzzle
 What
two shapes make a parallelogram?
 What other two pieces make this shape?
 Do they also work flipped over?
 Can you make a parallelogram with three
pieces?
 Hint:
Try pieces 1,2 and 5; make it in a different
way with these 3 pieces. Also try pieces
1,2, 5 flipped over
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BREAK Time !!
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 SVMI
morning sessions provide:
 Opportunities to experience the development
of specific mathematical content through the
grade levels.
 POMs
and Menu Slices provide:
multiple entry points to mathematics
 opportunity for extension, development, and
differentiation
 an opportunity to analyze and synthesize the
progression of mathematics within domains
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 September
 November
and October  POMs
and December  Menu Slices
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Geometry Menu Slices
 Choose
a color from the pile on your table.
 Go
to corresponding color Menu Station
 2- and 3- Dimensional Shapes
 Location and Position
 Transformations and Symmetry
 Visualization, Spatial Reasoning, and Modeling
 Work
through all the activities in the slice.
 Complete
the Learning Log
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Geometry Menu Slices
 Return
to your table.
 Share
Learning Log for the Slice you
experienced with your table.
 Whole
Group Discussion
Lunch
Please be back in 45 minutes
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Breakout Sessions
K-2
3-5
6-8
Algebra
- HS
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3-5 afternoon session
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Spatial Visualization
Number Talks
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Dot Patterns
•
2-D Geometry
•
3-D Geometry
Dot Patterns
How Many Dots?
How did you see it?
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2-D Geometry
What are the shapes?
How did you see them?
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3-D Geometry
How many cubes?
How did you see them?
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Teacher Techniques
• Individual Think Time
• Signals - e.g. Use of Thumbs
• Pair/Share
• Whole Group Share Out
• 3 x 5 Card Follow-up Question or Continuation for Next Day Number Talk
• 3 x 5 Card Formative Assessment: two different strategies for solving
problem
• And the conversation continues …
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Teacher Tools
• Overhead Transparencies
• Charts
• Butcher Paper Recordings
• White Boards
• Document Reader
• Smart Boards
• 3 x 5 Card Follow-up Question or Continuation for
Next Day Number Talk
• And the conversation continues …
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4 Triangle Problem
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Roping in Quadrilaterals
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MARS tasks related to Geometry
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MARS for next time (Measurement)
Work
the task
Think
about where your students will
be successful
Predict
misconceptions
Administer
Bring
the task to your students
back the work in December.